Difference between revisions of "2008 AMC 8 Problems/Problem 19"
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==Solution 1== | ==Solution 1== | ||
− | The two points are one unit apart at <math>8</math> places around the edge of the square. There are <math> | + | The two points are one unit apart at <math>8</math> places around the edge of the square. There are <math>8 \choose 2</math><math> = 28</math> ways to choose two points. The probability is |
<cmath>\frac{8}{28} = \boxed{\textbf{(B)}\ \frac27}</cmath> | <cmath>\frac{8}{28} = \boxed{\textbf{(B)}\ \frac27}</cmath> |
Revision as of 23:22, 7 January 2020
Contents
[hide]Problem
Eight points are spaced around at intervals of one unit around a square, as shown. Two of the points are chosen at random. What is the probability that the two points are one unit apart?
Solution 1
The two points are one unit apart at places around the edge of the square. There are ways to choose two points. The probability is
Solution 2
Arbitrarily pick a point in the grid. Clearly, we see two options for the other point to be placed, so the answer is
See Also
2008 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 18 |
Followed by Problem 20 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AJHSME/AMC 8 Problems and Solutions |
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